1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
library(psych)
library(whitening)
library("vioplot")
library("rpart")

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data Source https://archive.ics.uci.edu/ml/datasets/seeds

M. Charytanowicz, J. Niewczas, P. Kulczycki, P.A. Kowalski, S. Lukasik, S. Zak, ‘A Complete Gradient Clustering Algorithm for Features Analysis of X-ray Images’, in: Information Technologies in Biomedicine, Ewa Pietka, Jacek Kawa (eds.), Springer-Verlag, Berlin-Heidelberg, 2010, pp. 15-24.

1.2 The Data

seeds <- read.delim("~/GitHub/LatentBiomarkers/Data/seeds_dataset.txt", header=FALSE)
par(cex=0.5)

featnames <- c("area",
               "perimeter",
               "compactness",
               "length_of_kernel",
               "width_of_kernel",
               "asymmetry_coeff",
               "length_ker_groove",
               "class"
)
colnames(seeds) <- featnames
seeds$class <- 1*(seeds$class == 1)
pander::pander(table(seeds$class))

0	1
140	70

1.2.1 Standarize the names for the reporting

studyName <- "Seeds"
dataframe <- seeds
outcome <- "class"
thro <- 0.80
TopVariables <- 5
cexheat = 0.45

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
210	7

pander::pander(table(dataframe[,outcome]))

0	1
140	70


varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns


  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) > 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9943409

1.5 The decorrelation


DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 7 , Uni p: 0.03711537 , Uncorrelated Base: 2 , Outcome-Driven Size: 0 , Base Size: 2 
#> 
#> 
 1 <R=0.994,r=0.972,N=    3>, Top: 1( 1 )[ 1 : 1 Fa= 1 : 0.972 ]( 1 , 1 , 0 ),<|>Tot Used: 2 , Added: 1 , Zero Std: 0 , Max Cor: 0.971
#> 
 2 <R=0.971,r=0.935,N=    3>, Top: 1( 2 )[ 1 : 1 Fa= 1 : 0.935 ]( 1 , 2 , 1 ),<|>Tot Used: 4 , Added: 2 , Zero Std: 0 , Max Cor: 0.864
#> 
 3 <R=0.864,r=0.832,N=    4>, Top: 2( 1 )[ 1 : 2 Fa= 2 : 0.832 ]( 2 , 2 , 1 ),<|>Tot Used: 5 , Added: 2 , Zero Std: 0 , Max Cor: 0.825
#> 
 4 <R=0.825,r=0.800,N=    2>, Top: 1( 1 )[ 1 : 1 Fa= 2 : 0.800 ]( 1 , 1 , 2 ),<|>Tot Used: 5 , Added: 1 , Zero Std: 0 , Max Cor: 0.714
#> 
 5 <R=0.714,r=0.800,N=    0>
#> 
 [ 5 ], 0.7135263 Decor Dimension: 5 Nused: 5 . Cor to Base: 4 , ABase: 1 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

10.8

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

4.55

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

3.73

1.5.1 The decorrelation matrix


if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7135263

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data


if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate



univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")



univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

1.9.2 Final Table


univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##topfive
topvar <- c(1:length(varlist)) <= TopVariables
pander::pander(univarRAW$orderframe[topvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
asymmetry_coeff	2.67	1.1739	4.217	1.3818	9.80e-01	0.810
length_ker_groove	5.09	0.2637	5.569	0.5009	1.98e-03	0.764
compactness	0.88	0.0162	0.866	0.0254	5.69e-01	0.653
length_of_kernel	5.51	0.2315	5.689	0.5075	3.68e-04	0.562
perimeter	14.29	0.5766	14.692	1.5318	2.01e-05	0.524



topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]

theLaVar <- rownames(finalTable)[str_detect(rownames(finalTable),"La_")]

pander::pander(univarDe$orderframe[topLAvar,univariate_columns])

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
La_length_ker_groove	3.00	0.1832	3.365	0.1729	0.849	0.927
asymmetry_coeff	2.67	1.1739	4.217	1.3818	0.980	0.810
La_width_of_kernel	3.29	0.0455	3.255	0.0493	0.939	0.712
compactness	0.88	0.0162	0.866	0.0254	0.569	0.653
La_length_of_kernel	3.43	0.1286	3.504	0.1377	0.993	0.637


dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")

theSigDc <- dc[theLaVar]
names(theSigDc) <- NULL
theSigDc <- unique(names(unlist(theSigDc)))


theFormulas <- dc[rownames(finalTable)]
deFromula <- character(length(theFormulas))
names(deFromula) <- rownames(finalTable)

pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.5	4	0.571



allSigvars <- names(dc)



dx <- names(deFromula)[1]
for (dx in names(deFromula))
{
  coef <- theFormulas[[dx]]
  cname <- names(theFormulas[[dx]])
  names(cname) <- cname
  for (cf in names(coef))
  {
    if (cf != dx)
    {
      if (coef[cf]>0)
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("+ %5.3f*%s",coef[cf],cname[cf]))
      }
      else
      {
        deFromula[dx] <- paste(deFromula[dx],
                               sprintf("%5.3f*%s",coef[cf],cname[cf]))
      }
    }
  }
}

finalTable <- rbind(finalTable,univarRAW$orderframe[theSigDc[!(theSigDc %in% rownames(finalTable))],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- deFromula[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
La_length_ker_groove	-0.146area + 1.000length_ker_groove	3.00	0.1832	3.365	0.1729	8.49e-01	0.927	0.764	-1
asymmetry_coeff		2.67	1.1739	4.217	1.3818	9.80e-01	0.810	0.810	NA
length_ker_groove	NA	5.09	0.2637	5.569	0.5009	1.98e-03	0.764	0.764	NA
La_width_of_kernel	-0.204area + 0.540length_of_kernel + 1.000*width_of_kernel	3.29	0.0455	3.255	0.0493	9.39e-01	0.712	0.501	-2
compactness		0.88	0.0162	0.866	0.0254	5.69e-01	0.653	0.653	NA
La_length_of_kernel	-0.145area + 1.000length_of_kernel	3.43	0.1286	3.504	0.1377	9.93e-01	0.637	0.562	1
length_of_kernel	NA	5.51	0.2315	5.689	0.5075	3.68e-04	0.562	0.562	NA
area	NA	14.33	1.2157	15.104	3.4347	1.39e-05	0.515	0.515	4
width_of_kernel	NA	3.24	0.1776	3.266	0.4458	3.59e-03	0.501	0.501	NA

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,tol=0.002)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA


EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }


pander::pander(table(dataframe[,outcome],pr))

	0	1
0	134	6
1	21	49

pander::pander(ptab)

detail:

statistic	est	lower	upper
ap	0.2619	0.2038	0.3269
tp	0.3333	0.2700	0.4015
se	0.7000	0.5787	0.8038
sp	0.9571	0.9091	0.9841
diag.ac	0.8714	0.8185	0.9135
diag.or	52.1111	19.8637	136.7104
nndx	1.5217	1.2692	2.0504
youden	0.6571	0.4877	0.7879
pv.pos	0.8909	0.7775	0.9589
pv.neg	0.8645	0.8004	0.9141
lr.pos	16.3333	7.3559	36.2669
lr.neg	0.3134	0.2188	0.4491
p.rout	0.7381	0.6731	0.7962
p.rin	0.2619	0.2038	0.3269
p.tpdn	0.0429	0.0159	0.0909
p.tndp	0.3000	0.1962	0.4213
p.dntp	0.1091	0.0411	0.2225
p.dptn	0.1355	0.0859	0.1996

tab:

Outcome + Outcome - Total

Test + 49 6 55

Test - 21 134 155

Total 70 140 210
method: exact
digits: 2
conf.level: 0.95

	Outcome +	Outcome -	Total
Test +	49	6	55
Test -	21	134	155
Total	70	140	210

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.871	0.818	0.914
3	se	0.700	0.579	0.804
4	sp	0.957	0.909	0.984
6	diag.or	52.111	19.864	136.710


par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	130	10
1	7	63

pander::pander(ptab)

detail:

statistic	est	lower	upper
ap	0.3476	0.2834	0.416
tp	0.3333	0.2700	0.401
se	0.9000	0.8048	0.959
sp	0.9286	0.8726	0.965
diag.ac	0.9190	0.8736	0.952
diag.or	117.0000	42.5430	321.768
nndx	1.2069	1.0822	1.476
youden	0.8286	0.6773	0.924
pv.pos	0.8630	0.7625	0.932
pv.neg	0.9489	0.8976	0.979
lr.pos	12.6000	6.8989	23.012
lr.neg	0.1077	0.0532	0.218
p.rout	0.6524	0.5838	0.717
p.rin	0.3476	0.2834	0.416
p.tpdn	0.0714	0.0348	0.127
p.tndp	0.1000	0.0412	0.195
p.dntp	0.1370	0.0677	0.238
p.dptn	0.0511	0.0208	0.102

tab:

Outcome + Outcome - Total

Test + 63 10 73

Test - 7 130 137

Total 70 140 210
method: exact
digits: 2
conf.level: 0.95

	Outcome +	Outcome -	Total
Test +	63	10	73
Test -	7	130	137
Total	70	140	210

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.919	0.874	0.952
3	se	0.900	0.805	0.959
4	sp	0.929	0.873	0.965
6	diag.or	117.000	42.543	321.768


par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	138	2
1	23	47

pander::pander(ptab)

detail:

statistic	est	lower	upper
ap	0.2333	0.17789	0.2965
tp	0.3333	0.26996	0.4015
se	0.6714	0.54878	0.7791
sp	0.9857	0.94935	0.9983
diag.ac	0.8810	0.82929	0.9215
diag.or	141.0000	32.02203	620.8538
nndx	1.5217	1.28648	2.0075
youden	0.6571	0.49813	0.7773
pv.pos	0.9592	0.86021	0.9950
pv.neg	0.8571	0.79339	0.9072
lr.pos	47.0000	11.75707	187.8870
lr.neg	0.3333	0.23833	0.4662
p.rout	0.7667	0.70353	0.8221
p.rin	0.2333	0.17789	0.2965
p.tpdn	0.0143	0.00173	0.0507
p.tndp	0.3286	0.22095	0.4512
p.dntp	0.0408	0.00498	0.1398
p.dptn	0.1429	0.09276	0.2066

tab:

Outcome + Outcome - Total

Test + 47 2 49

Test - 23 138 161

Total 70 140 210
method: exact
digits: 2
conf.level: 0.95

	Outcome +	Outcome -	Total
Test +	47	2	49
Test -	23	138	161
Total	70	140	210

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.881	0.829	0.921
3	se	0.671	0.549	0.779
4	sp	0.986	0.949	0.998
6	diag.or	141.000	32.022	620.854



par(op)

1.11.1 EFA


  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }


  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	133	7
1	12	58

  pander::pander(ptab)

detail:

statistic	est	lower	upper
ap	0.3095	0.2477	0.377
tp	0.3333	0.2700	0.401
se	0.8286	0.7197	0.908
sp	0.9500	0.8997	0.980
diag.ac	0.9095	0.8623	0.945
diag.or	91.8333	34.4026	245.137
nndx	1.2844	1.1264	1.615
youden	0.7786	0.6194	0.888
pv.pos	0.8923	0.7906	0.956
pv.neg	0.9172	0.8599	0.957
lr.pos	16.5714	7.9870	34.382
lr.neg	0.1805	0.1077	0.302
p.rout	0.6905	0.6232	0.752
p.rin	0.3095	0.2477	0.377
p.tpdn	0.0500	0.0203	0.100
p.tndp	0.1714	0.0918	0.280
p.dntp	0.1077	0.0444	0.209
p.dptn	0.0828	0.0435	0.140

tab:

Outcome + Outcome - Total

Test + 58 7 65

Test - 12 133 145

Total 70 140 210
method: exact
digits: 2
conf.level: 0.95

	Outcome +	Outcome -	Total
Test +	58	7	65
Test -	12	133	145
Total	70	140	210

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.910	0.862	0.945
3	se	0.829	0.720	0.908
4	sp	0.950	0.900	0.980
6	diag.or	91.833	34.403	245.137

  par(op)

Decorrelation-Based Feature Discovery: Seeds

Jose Tamez

2023-09-12

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

1.1 Material and Methods

1.2 The Data

1.2.1 Standarize the names for the reporting

1.3 Generaring the report

1.3.1 Libraries

1.3.2 Data specs

1.3.3 Scaling the data

1.4 The heatmap of the data

1.4.0.1 Correlation Matrix of the Data

1.5 The decorrelation

1.5.1 The decorrelation matrix

1.6 The heatmap of the decorrelated data

1.7 The correlation matrix after decorrelation

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

1.8.2 The decorralted UMAP

1.9 Univariate Analysis

1.9.1 Univariate

1.9.2 Final Table

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

1.10.2 EFA

1.11 Effect on CAR modeling

1.11.1 EFA